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The number of real roots of 3^x+4^x+5^x-6^x=0 is?

The number of real roots of 3^x+4^x+5^x-6^x=0 is?

Grade:Upto college level

1 Answers

Rahul askIITiansExpert.IITR
110 Points
10 years ago
this question can be exactly solved by drawing the graphs of functions: y=3^x, 4^x, 5^x and 6^x.

now consider this following arguement

1. they all will coinside at the point x=0, where there value is 1.

2. after that each of them continuosly increasing which their own pace.

3. it will be true(if it is) that there values at particular x satisfy the equation only once.

so the number of real roots should be 1.

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